The present application relates to the use of a technique called “companding” with digital signal processing. More specifically, the present application relates to using companding to resize the dynamic range of an input signal so that the signal is better suited for processing by a digital signal processor (DSP).
There are typically two types of DSPs, floating-point DSPs and fixed-point DSPs. Generally, a floating-point DSP uses a certain number of bits to represent the mantissa of a signal's value and another set of bits to represent the exponent of the signal's value. For example, for a large signal, which may be quantified as 1126.4, which is 1.1 times 210, a floating point representation may be 1.1 for the mantissa and 10 for the exponent. Floating-point DSPs thus provide the ability to represent a very wide range of values, but with a precision that is limited by the number of bits used to represent the mantissa.
Unlike a floating-point DSP, a fixed-point DSP uses all of its bits to represent a signal's value. The precision of the fixed-point DSP is determined by dividing its range by the number of discrete values that can be represented by the available bits in the DSP. Thus, for example, if a DSP is to process signals having a range of 0-16 and it has three available bits, which can represent eight discrete values, then the least significant bit carries a value of two. Fixed-point DSPs can experience problems, however, with signals that are not sized well to the DSP. For example, in a 21-bit fixed point system, if the least significant bit is set to 1, the DSP that can only handle signals having values up to 2,097,152, so a signal with the value of 3,676,000 will not be properly processed. As another example, if the signal's value is small (e.g., 10) and changes to the signal's value are small (e.g., +/−1.4) compared to the range of the fixed-point DSP (e.g., 2,097,152), quantization noise from rounding problems may result in a degradation of signal quality because the least significant bit is larger than, or a large portion of, the changes to the signal's value. In contrast, in a floating-point DSP, the mantissa and exponent may be used to represent decimal values so that rounding errors are minimized.
Currently, floating-point DSPs are used in applications where the range of a signal's value varies. This is because the floating-point DSPs can adjust to the change in range by using exponent bits. Nevertheless, it is often desirable to use fixed-point DSPs instead, because fixed-point DSPs typically consume less power, are cheaper, and are fabricated in less chip area compared to floating-point DSPs.
Therefore, it is desirable to provide fixed-point DSPs that can be used in applications where the range of a signal's value varies, without the problems typically associated with fixed-point DSPs, such as significant quantization noise or overflow.